Laws of Motion & Friction · JEE Main previous year questions

A block of mass $\mathrm{M}$ slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta$. The magnitude of the contact force will be :

1. A.$\mathrm{Mg}$
2. B.$\mathrm{Mg}\cos \theta$
3. C.$\sqrt{\mathrm{Mg}\sin \theta +\mathrm{Mg}\cos \theta }$
4. D.$\mathrm{Mg}\sin \theta \sqrt{1+\mu }$

A block 'A' takes $2\mathrm{s}$ to slide down a frictionless incline of $30^{\circ }$ and length 'l', kept inside a lift going up with uniform velocity 'v'. If the incline is changed to $45^{\circ }$, the time taken by the block, to slide down the incline, will be approximately :

1. A.$2.66\mathrm{s}$
2. B.$0.83\mathrm{s}$
3. C.$1.68\mathrm{s}$
4. D.$0.70\mathrm{s}$

A wire of length $30\mathrm{cm}$, stretched between rigid supports, has it's $n^{\mathrm{th}}$ and $(n+1{)}^{\mathrm{th}}$ harmonics at $400\mathrm{Hz}$ and $450\mathrm{Hz}$, respectively. If tension in the string is $2700\mathrm{N}$, it's linear mass density is ____ $kg/m$.

1. A.$3360\mathrm{N}$
2. B.$3380\mathrm{N}$
3. C.$3120\mathrm{N}$
4. D.$3240\mathrm{N}$

1. A.$10\mathrm{N}$
2. B.$20\mathrm{N}$
3. C.$25\mathrm{N}$
4. D.$45\mathrm{N}$

Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :

1. A.4 : 5
2. B.2 : 5
3. C.5 : 4
4. D.5 : 2

A block of mass $2\text{ kg}$ moving on a horizontal surface with speed of $4{\text{ ms}}^{-1}$ enters a rough surface ranging from $x=0.5\text{ m}$ to $x=1.5\text{ m}$. The retarding force in this range of rough surface is related to distance by $F=-kx$ where $k=12{\text{ Nm}}^{-1}$. The speed of the block as it just crosses the rough surface will be :

1. A.zero
2. B.$1.5{\text{ ms}}^{-1}$
3. C.$2.0{\text{ ms}}^{-1}$
4. D.$2.5{\text{ ms}}^{-1}$

1. A.$\frac{6}{\sqrt{110}}$
2. B.$\frac{3}{\sqrt{113}}$
3. C.$\frac{3}{\sqrt{109}}$
4. D.$\frac{2}{\sqrt{109}}$

1. A.$9.8\mathrm{N}$
2. B.$39.2\mathrm{N}$
3. C.$49\mathrm{N}$
4. D.$78.4\mathrm{N}$

The velocity of a small ball of mass '$m$' and density $d_1$, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is $d_2$, then the viscous force acting on the ball, will be :

1. A.$mg\left(1-\frac{d_1}{d_2}\right)$
2. B.$mg\left(1-\frac{d_2}{d_1}\right)$
3. C.$mg\left(\frac{d_1}{d_2}-1\right)$
4. D.$mg\left(\frac{d_2}{d_1}-1\right)$

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x(u^2-gL)}$. The value of $x$ is -

1. A.$3$
2. B.$2$
3. C.$1$
4. D.$5$

1. A.
2. B.
3. C.
4. D.

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of $15{\text{ ms}}^{-1}$. The impulse imparted to the ball is ________ Ns.

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ___________ m.

A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

1. A.the same throughout the motion.
2. B.minimum at the highest position of the circular path.
3. C.minimum at the lowest position of the circular path.
4. D.minimum when the rope is in the horizontal position.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y=\left(10\cos \pi x\sin \frac{2\pi t}{T}\right)\mathrm{cm}$ The amplitude of the particle at $x=\frac{4}{3}\mathrm{cm}$ will be ____ $\mathrm{cm}$.

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of $0.8\sqrt{gh}$. The value of work done by the air-friction is :

1. A.$-0.68\mathrm{mgh}$
2. B.$\mathrm{mgh}$
3. C.$1.64\mathrm{mgh}$
4. D.$0.64\mathrm{mgh}$

1. A.$\frac{4}{3}g$
2. B.$\frac{6}{5}g$
3. C.$\frac{3}{5}g$
4. D.$\frac{2}{3}g$